Definition A.2 ([1]})
For any \(M\in {\rm Sp}(2n)\)  and \({\omega }\in {\bf U}\) , choosing \(\tau >0\)  and \({\gamma }\in {\cal P}_\tau (2n)\)  with \({\gamma }(\tau )=M\) ,
we define
\(S_M^{\pm }({\omega })=\lim _{\epsilon \rightarrow 0^+}\;i_{\exp (\pm \epsilon \sqrt{-1}){\omega }}({\gamma })-i_{\omega }({\gamma }).\) 
